On the spinor zeta functions problem: higher power moments of the Riesz mean

Haiyan Wang. "On the spinor zeta functions problem: higher power moments of the Riesz mean." Acta Arithmetica 157.3 (2013): 231-248. <http://eudml.org/doc/279341>.

@article{HaiyanWang2013,
abstract = {Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp₂(ℤ) of genus 2. The coefficients of the spinor zeta function $Z_F(s)$ are denoted by cₙ. Let $D_ρ(x;Z_F)$ be the Riesz mean of cₙ. Kohnen and Wang obtained the truncated Voronoï-type formula for $D_ρ(x;Z_F)$ under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of $D_ρ(x;Z_F)$, and then derive an asymptotic formula for the hth (h=3,4,5) power moments of $D₁(x;Z_F)$ by using Ivić’s large value arguments and other techniques.},
author = {Haiyan Wang},
journal = {Acta Arithmetica},
keywords = {Riesz mean; spinor zeta function; power moment},
language = {eng},
number = {3},
pages = {231-248},
title = {On the spinor zeta functions problem: higher power moments of the Riesz mean},
url = {http://eudml.org/doc/279341},
volume = {157},
year = {2013},
}

TY - JOUR
AU - Haiyan Wang
TI - On the spinor zeta functions problem: higher power moments of the Riesz mean
JO - Acta Arithmetica
PY - 2013
VL - 157
IS - 3
SP - 231
EP - 248
AB - Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp₂(ℤ) of genus 2. The coefficients of the spinor zeta function $Z_F(s)$ are denoted by cₙ. Let $D_ρ(x;Z_F)$ be the Riesz mean of cₙ. Kohnen and Wang obtained the truncated Voronoï-type formula for $D_ρ(x;Z_F)$ under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of $D_ρ(x;Z_F)$, and then derive an asymptotic formula for the hth (h=3,4,5) power moments of $D₁(x;Z_F)$ by using Ivić’s large value arguments and other techniques.
LA - eng
KW - Riesz mean; spinor zeta function; power moment
UR - http://eudml.org/doc/279341
ER -